Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?

TL;DR

This paper derives a microscopic expression for the chemical potential in active Brownian particles, demonstrating its spatial constancy in steady states and establishing conditions for phase coexistence, bridging active matter and thermodynamic concepts.

Contribution

It introduces a novel microscopic chemical potential for active particles, including an activity-induced swim potential, and validates it through simulations and theoretical calculations.

Findings

Chemical potential remains spatially constant in steady active fluids.

Phase coexistence involves both mechanical and diffusive equilibrium.

Bulk chemical potential and pressure describe phase behavior at low activity.

Abstract

We derive a microscopic expression for a quantity $\mu$ that plays the role of chemical potential of Active Brownian Particles (ABPs) in a steady state in the absence of vortices. We show that $\mu$ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on active Brownian particles show good agreement with our Fokker-Planck calculations, and confirm that $\mu(z)$ is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.